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Cut Vertices in Random Planar Maps

Authors Michael Drmota , Marc Noy , Benedikt Stufler

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  • 18 pages

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Author Details

Michael Drmota
  • TU Wien, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstrasse 8 - 10, A-1040 Vienna, Austria
Marc Noy
  • Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada II, Jordi Girona 1 - 3, 08034 Barcelona, Spain
Benedikt Stufler
  • Universität München, Mathematisches Institut, Theresienstr. 39, 80333 Munich, Germany


We thank the referees for their careful reading and their valuable comments for improving the presentation.

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Michael Drmota, Marc Noy, and Benedikt Stufler. Cut Vertices in Random Planar Maps. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 10:1-10:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


The main goal of this paper is to determine the asymptotic behavior of the number X_n of cut-vertices in random planar maps with n edges. It is shown that X_n/n → c in probability (for some explicit c>0). For so-called subcritial subclasses of planar maps like outerplanar maps we obtain a central limit theorem, too.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Random graphs
  • random planar maps
  • cut vertices
  • generating functions
  • local graph limits


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